Abstract
In this note, we give a simple extension map from partitions of subsets of [n] to partitions of [n+1], which sends δ-distant k-crossings to (δ+1)-distant k-crossings (and similarly for nestings). This map provides a combinatorial proof of the fact that the numbers of enhanced, classical, and 2-distant k-noncrossing partitions are each related to the next via the binomial transform. Our work resolves a recent conjecture of Zhicong Lin and generalizes earlier reduction identities for partitions.
Original language | English (US) |
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Article number | 111705 |
Journal | Discrete Mathematics |
Volume | 343 |
Issue number | 6 |
DOIs | |
State | Published - Jun 2020 |
All Science Journal Classification (ASJC) codes
- Theoretical Computer Science
- Discrete Mathematics and Combinatorics